In addition to the liquid fuel volume, fuel tanks also contain a gas volume, which is formed by fuel vapors and/or air. Temperature fluctuations lead to corresponding internal-pressure fluctuations in the tank. Excess pressures which occur have to be reduced, but emission regulations mean that fuel vapors must not escape into the atmosphere. The pressure is therefore reduced via an activated carbon filter (ACF) into which a vent line leads. However, it has to be ensured that liquid fuel does not pass into the activated carbon filter via the vent line. Up to now, a valve, for example a float valve, has therefore been arranged at the inlet opening of the vent line, the valve closing in the presence of liquid fuel, such as may occur if the vehicle is on a slope and/or during sloshing of the fuel. To ensure that the fuel tank can be vented during a wide range of circumstances which occur, two or more venting locations are provided with corresponding lines and valves, with the result that if one valve dips into liquid fuel, another valve, which is preferably arranged in the opposite region of the tank, may be open. These valves are subject to mechanical faults and cause additional costs during production of the fuel tank.